Question

The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this information at certain times during a given day. The following temperatures were recorded on a January day in New York City.Time of Day10 AM12 Noon2 PM4 PM6 PM8 PM10 PMTemperature ((Degrees Fahrenheit))30353636343028 What is the average rate of change of temperature with respect to time over the evening hours from 6 PM to 10 PM? Interpret this value in a complete sentence.a.6 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 6 degrees per hour from 6 PM to 10 PM.b.Negative 6 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 6 degrees per hour from 6 PM to 10 PM.c.Negative 1.5 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour from 6 PM to 10 PM.d.1.5 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour from 6 PM to 10 PM.

Answer 1

The average rate of change of temperature with respect to time over the evening hours from 6 PM to 10 PM is -1.5 degrees per hour.

Step-by-step explanation:

To find the average rate of change of temperature with respect to time over the evening hours from 6 PM to 10 PM, we need to calculate the difference in temperature and time between these two points.

The temperature at 6 PM is 34°F, and the temperature at 10 PM is 28°F. The time difference between 6 PM and 10 PM is 4 hours.

To calculate the average rate of change, we divide the difference in temperature by the time difference: (28 - 34) / 4 = -6 / 4 = -1.5

Therefore, the average rate of change of temperature with respect to time over the evening hours from 6 PM to 10 PM is -1.5 degrees per hour. This means that on average, the temperature drops at a rate of 1.5 degrees per hour during this time period.

Answer 2

Step-by-step explanation:

Here, with the given values, we want to interpret how temperature has changed from 6pm upwards

From what we have on the table, starting from 6pm, there was a 6 degree Fahrenheit drop in temperature

This happened over 4 hours

Now, to get the hourly drop, we have to divide this total drop by the number of hours

Mathematically, we have this as:

`\frac{28\degree F-34\degree F}{10\text{ - 6}}\text{ = }(-6\degree F)/(4)\text{ = -15}\degree F\text{ per hour}`